2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126834The asymptotic dimension theory was founded by Gromov in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups.Added some remarks about coarse equivalence of finitely generated groups.Geometric TopologyGroup Theory55M10; 20F69text